Question

find the sum of first 30 terms of an AP whose Nth term is 2-3n.​

Answer 1

Answer:

It is given that the nth term of A.P is Tn=3+2n.

We know that the general term of an arithmetic progression with first term a and common difference d is Tn=a+(n−1)d, therefore,

Tn=3+2n=5+(n−1)2

Comparing the above term by the general term of A.P, we get a=5 and d=2

We also know that the sum of an arithmetic series with first term a and common difference d is Sn=2n[2a+(n−1)d]

Now to find the sum of first 30 terms of an A.P, substitute n=30,a=5 and d=2 in Sn=2n[2a+(n−1)d] as follows:

S30=230[(2×5)+(30−1)2]=15[10+(29×2)]=15(10+58)=15×68=1020

Hence, the sum of first 30 terms is 1020